Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our findings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.Comment: 14 page

Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our ?ndings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.optimal execution, market impact, ordinary di?erential equations

Investigation of the rotor–obstacle aerodynamic interaction in hovering flight

In this paper, a comprehensive experimental survey of the aerodynamic interaction of a hovering rotor in the proximity of a ground obstacle is described, taking advantage of multiple experimental techniques. Load measurements on the rotor were carried out to assess the change in the rotor performance for different positions with respect to the cubic obstacle, thus simulating a set of possible hovering flight conditions around the obstacle. Laser Doppler anemometry measurements of the rotor inflow were used to investigate how the aerodynamic interaction affected the rotor performance. Stereoscopic particle image velocimetry measurements in the region between the rotor and the obstacle were carried out to gain a better insight of the interacting flow field. The investigation showed two main regions of interest. The first region is the one above the edge of the obstacle, where the rotor experiences a gradual ground effect as it is positioned over the obstacle. The second region, probably of more interest, is the one just beside the obstacle where a recirculation region between the rotor and the obstacle develops, causing both a significant reduction in the thrust augmentation experienced in unobstructed hover in ground effect and significant pitching and rolling moments, due to the nonsymmetrical inflow pattern on the rotor

Optimal trading execution with nonlinear market impact: an alternative solution method

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our findings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.optimal execution; market impact; ordinary differential equations

Rotor-Obstacle Aerodynamic Interaction in Hovering Flight: An Experimental Survey

Despite the presence of a fair number of numerical and experimental works on the rotor-obstacle interaction, a systematic study of the aerodynamic phenomena involved is lacking. In this paper a comprehensive experimental survey carried out at University of Glasgow is described, taking advantage of two different rotor rigs and several experimental techniques. Load measurements on the rotor were carried out in order to assess the rotor performance for different positions with respect to a cubic obstacle, thus simulating a set of possible hovering flight conditions around the obstacle. Laser Doppler Anemometry (LDA) measurements of the rotor inflow were used in order to investigate how the aerodynamic interaction affected the rotor performance. Eventually Stereoscopic Particle Image Velocimetry (SPIV) measurements in the region between the rotor and the obstacle were carried out in order to have a better insight of the interacting flow field

Towards a Wind Tunnel Testing Environment for Rotorcraft Operations Close to Obstacles

The correct identification of the aerodynamic loads due to interaction between rotorcraft and obstacles requires to run computationally intensive numerical models characterized by a high level of uncertainty. Wind tunnel data can be used as a source of information to improve those models. The present paper investigates the aerodynamic interaction of a helicopter and ship airwake exploiting wind tunnel data. A series of wind tunnel experiment, using a scaled helicopter model and Simple Frigate Shape 1, has been performed to measure forces and moments acting on the rotor, while the helicopter is approaching the flight deck. In addition, the velocity components along the longitudinal symmetry plane of the rotor have been visualized using PIV technique. With the rotor positioned at the starting point of the landing trajectory, the load measurements are used to modify the distribution of the inflow over the rotor in multibody simulation environment, in order to generate same loads, including thrust, torque and in-plane moments. Then, an identification algorithm is developed to capture the effect of ship airwake on the rotor loads during the maneuvers, modeling it as an external gust to the rotor inflow. The gust velocity is obtained through an optimization algorithm with the objective of generating same load coefficients as the experiment. The simulation results show that the same load coefficients as the experiment can be generated by implementing a linear gust over the rotor with a magnitude that changes as the rotor moves through the wake of ship. The experiment showed that this test setup could be used for identification of aerodynamic interaction to be used for maneuver analysis

Experimental Investigation on the Aerodynamic Interaction Between a Helicopter and Ground Obstacles

In this study, experiments were performed to investigate the aerodynamic interaction between a helicopter and ground obstacles. A new experimental set-up was realised and validated. The motorised helicopter model, which included the fuselage, was positioned in different positions relative to a model building in order to replicate different hovering configurations. The use of a helicopter model with a six-component balance and a building model with several pressure taps allowed a database to be compiled for the loads on the helicopter and obstacle. First several tests were performed without the building in order to develop a reference database and assess the experimental set-up through a comparison with results in the literature. The measured loads were analysed to investigate the interference effects of the building model on the helicopter performance. A physical interpretation of the flow phenomena was obtained through analysis of the obstacle pressure measurements and particle image velocimetry surveys of relevant configurations

Optimal trading execution with nonlinear market impact: an alternative solution method

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our findings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period

Particle Image Velocimetry (PIV) experimental study on the buoyant flow fields within a thermal chimney system for geothermal power plant

To enhance the air-cooling process in geothermal power plants for economical utilization of the exhaust steam from expansion, a natural-draft thermal chimney design was proposed and studied here in this paper. In view of the necessity of accurate velocity field measurements which would provide further insight into the physics behind the evolving plumes above heated horizontal cylinders, Particle Image Velocimetry (PIV) was employed to experimentally investigate the buoyant flow in the thermal chimney system. Two configurations have been tested to understand the flow induced by the horizontally heated cylinders inside the thermal chimney. Firstly, flow field above a single row of cylinders was tested while they were isothermally heated to simulate of an air-cooled condenser. After that, a second row of cylindrical heaters (air-heater) was added above the first row to enhance the buoyant flow, aiming at enhancing the air side flow of the air-cooled condenser. Flow characteristics and velocity enhancement were studied for both configurations. The results show that significant flow unsteadiness occur near the cylindrical heaters because of the non-steady crossing flows between adjacent cylinders, and the unsteadiness attenuates in the downstream. The effects of cylinder row distance, surface temperature as well as downstream distance on the flow field were then analyzed. Flow velocity is increased by the air-heater as the buoyancy force is enhanced, proving the idea of flow enhancement of the thermal chimney configuration. It is also observed that the velocity fluctuation, turbulent kinetic energy and vorticity change significantly after adding the second row of heaters. The present study provides further insight into natural convection flow theory of heated cylinders for a Rayleigh number range of 1.3E4 to 2.2E4, which is fundamental for the flow enhancement designing of the proposed natural-convection-driven cooling system

Modal characterisation of a rotor/propeller rig for tip-mach scaled wind tunnel testing

An advanced rotor and propeller rig for tip Mach-scaled wind tunnel testing is the subject of dynamic analysis presented in this paper. Experimental modal analysis and finite element method are used to assess the key characteristics such as the modal properties and transfer functions, as well as their changes under varying conditions. This work aims to determine and summarize these characteristics for the purposes of further rig development and its safe operation. The research also includes analysis of the key sources of uncertainty, damping, the effect of unbalanced excitation and model-experiment correlation. The low frequency region is found to be dominated by the three weakly damped global modes whilst the following modes feature increased modal activity of the rotor shaft and the hub. The latter set of modes is also found to be more susceptible to nonlinear effects and associated increased identification and modelling uncertainty